1. Field of the Invention
The present invention relates to an apparatus and method for apodization measurement in a lithographic apparatus.
2. Background of the Related Art
A lithographic apparatus is a machine that applies a desired pattern onto a target portion of a substrate. Lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that circumstance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern corresponding to an individual layer of the IC, and this pattern can be imaged onto a target portion (e.g. comprising part of, one or several dies) on a substrate (e.g. a silicon wafer) that has a layer of radiation-sensitive material (resist). In general, a single substrate will contain a network of adjacent target portions that are successively exposed. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the pattern through the projection beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction.
We first discuss here some background concerning lens apodization.
Lens light non-uniformity is in general characterized in the image plane. Very tight specifications are used in order to limit CD-variations (critical dimension variations) through the image field. When light non-uniformity appears in the pupil plane, (e.g. over the various angles at image level), CD-variations through pitch are expected. Light non-uniformity in the pupil is often referred to as apodization. In this sense, apodization describes the amplitude part of the pupil-transmission function (where aberrations describe the phase part of the pupil transmission function). A uniform pupil transmission is often assumed, but this is generally not the case.
Below we give a definition of lens apodization and its relation to pupil measurement. Next we give an overview of the different types of apodization and their impact on imaging.
Mathematically imaging can be described by two Fourier transforms: one from the object plane to the pupil plane and one from the pupil plane to the image plane. Prior to the second Fourier transform, the pupil distribution must be multiplied by the OTF (optical transfer function) of the imaging system.
      I    ⁡          (              x        ->            )        =            ∫              ρ        ->              ⁢                  OTF        ⁡                  (                                    x              ->                        ,                          ρ              ->                                )                    ·              [                              ∫                          x              ->                                                                      ⁢                                    O              ⁡                              (                                                      x                    ->                                    ′                                )                                      ·                          ⅇ                              2                ·                π                ·                i                ·                                                      x                    ->                                    ′                                ·                                  ρ                  ->                                                                    ⁢                                  ]            ⁢                          ·              ⅇ                              -            2                    ·          π          ·          i          ·                                    x              ->                        ′                    ·                      ρ            ->                              
Here, I and O equal the E-fields in the image and object planes as function of the field co-ordinates {right arrow over (x)}, and pupil co-ordinates {right arrow over (ρ)}. In order to obtain the image intensity, the amplitude of the E-field needs to be squared.
The OTF can be split into a phase term W (describing the aberrations)
      OTF    ⁡          (                        x          ->                ,                  ρ          ->                    )        =            A      ⁡              (                              x            ->                    ,                      ρ            ->                          )              ·          ⅇ                        -          2                ·        π        ·        i        ·                  W          ⁡                      (                                          x                ->                            ,                              ρ                ->                                      )                              and an apodization term A (describing the apodization). Both are a function of the pupil co-ordinate {right arrow over (ρ)}, and vary over the field with field co-ordinates {right arrow over (x)}.
Next we turn to an apodization definition. Apodization is defined as the angular lens transmission. The apodization function A(r) can be decomposed into several classes of functions. In analogy with aberrations Zernike polynomials Zn({right arrow over (ρ)}) and the corresponding Zernike coefficients zn({right arrow over (x)}) are an appropriate decomposition.
      A    ⁡          (                        x          ->                ,                  ρ          ->                    )        =            ∑      n        ⁢                            z          n                ⁡                  (                      x            ->                    )                    ·                        Z          n                ⁡                  (                      ρ            ->                    )                    
These Zernike coefficients have no dimension, representing the transmission of the corresponding Zernike polynomial at the pupil-edge.
In line with the assumption of uniform lens transmission, lens apodization is currently typically not measured directly. Various components of it are part of or influence other measurements. E.g. the uniform pupil transmission Z1(x) is part of the uniformity measurement.
Current pupil measurements at wafer-level measure a combination of the illumination angular intensity and the lens apodization. No separation is made between lens and illuminator effects. This can be dangerous since both induce different imaging effects.
To understand the impact on imaging, one has to look at the diffraction pattern of the object. In general, large objects have small diffraction patterns, while small objects have large diffraction patterns. Diffraction patterns are (in general) symmetric; the amplitude of the positive diffraction orders is equal to the amplitude of the negative diffraction orders.
Odd apodizations affect the telecentricity of the light at wafer level. Telecentricity equals the mean pointing (i.e. mean direction) of the imaging beam. In this way it affects overlay as a function of focus. That is to say, for odd apodizations more light reaches a given point on the wafer (image plane) from one side than from the other, with the result that if the wafer is moved up or down with respect to the image plane (thus defocusing the exposed image) the image effectively moves horizontally.
Even apodizations (for which the light intensity reaching a given point on the wafer (image plane) is symmetrical about a line perpendicular to the wafer) affect the optimal exposure dose as a function of structure density (pitch) and orientation. Thus it results in CD variations through pitch; lines of different pitch require a different exposure dose to be printed at the same size.
As a special case, astigmatic apodization introduces an energy difference between horizontal and vertical lines.
Apodization appears within the lens pupil. Thus it can only be measured with a pupil sensor. One can use e.g. a pinhole sensor scanning at large defocus, or a parallel detector array, conjugate with the pupil plane. All such sensors contain optical interfaces and/or may not be perfectly conjugate with the pupil and thus need to be corrected for geometrical effects as well as angular transmission effects (Fresnel coefficients).
In an optical context conjugate points are points on the optical axis of an optical system, such as a lens or mirror, so positioned that light emitted from either point will be focused at the other, e.g. object and image points. By extension, conjugate planes are planes normal to the optical axis of an optical system so positioned that light emitted from points in either plane will be focused at the other, e.g. object and image planes.
Next one has to realise a known pupil filling at object level. This can be either realised by calibrating or measuring a well-defined intensity distribution, or by use of a theoretically known intensity distribution such as given by a perfect pinhole, with a diameter small with respect to the wavelength used.
US 2002/0001088 (corresponding to WO 01/63233 in the name of Carl Zeiss) describes an apparatus for wavefront detection which includes an optical system for transforming a wavefront, a diffraction grating through which the wavefront passes, and a spatially resolving detector following the diffraction grating. FIG. 1 of the Zeiss patent shows the layout of the apparatus, in which light from a source 43 passes through a movable light guide 29, a perforated mask 8, lenses 13 and 15, and a moveable diffraction grating 11 before reaching a detector 19 which comprises a sensor surface 20. The apparatus of the Zeiss patent can be used for the measurement of lens aberration. The function of the grating 11 is to convert phase effects (caused by aberrations) to amplitude effects, which are then measured by the detector 19. In the Zeiss patent scanning is also required because it is necessary to separate x and y components. The scanning allows one component to be averaged out so that the other can be measured.